Besides two-mode EPR steering, the multipartite EPR steering has also been
widely investigated since it has potential application in quantum network.
Genuine multipartite steering exists if it can be shown that a steering
nonlocality is necessarily shared among all observers [1]}. The
criterion for multipartite EPR steering and for genuine multipartite EPR
steering has been developed [2]}, [1]}. Genuine high-order EPR
steering has also been experimentally demonstrated [4]}.
Multipartite Gaussian EPR steering in Greenberger-Horne-Zeilinger (GHZ)
state [5]}, [6]} and a four-mode cluster state [7]} have
been demonstrated. The experiments of multipartite Gaussian EPR steering
only demonstrated EPR steering in the case of bipartite splitting at
present, while genuine multipartite EPR steering for Gaussian states has not
been demonstrated. Recently, the distribution of multipartite steering in a
quantum network by separable states has been demonstrated [8]}, [9]}.
